Search results for "Numerical Analysis"

Numerical approach to the exact controllability of hyperbolic systems

2005

In this paper we present the numerical implementation of H.U.M. (Hilbert Uniqueness Method, J.L.Lions[1]). We restrict ourselves to the exact boundary controllability of the wave equation, with Dirichlet controls, but the numerical method presented here can be applied to other kinds of controllability. The problem is discretized by a finite elements of first order in space and by a discrete time Galerkin approximation (Dupont [1]). The efficiency of the method is illustrated by numerical results.

Modelling of EM glass convection

2008

PurposeTo develop the mathematical model, which allows predicting the temperature and flow distribution of an opaque glass melt with the temperature‐dependent properties in case it is generated by electromagnetic and thermal convection. Analysis has been done for geometry of the model crucible with the immersed rod electrodes. Numerical analysis is used as a tool for finding out the parameters of the system, which allow getting desiderated homogeneity of temperature field by EM action.Design/methodology/approachANSYS CFX software is implemented for coupling of EM, thermal and HD processes in the modelled system. Usability of non‐inductive approximation is shown using a full harmonic analysi…

Fronts propagating with signal dependent speed in limited diffusion and related Hamilton-Jacobi formulations

2021

We consider a class of limited diffusion equations and explore the formation of diffusion fronts as the result of a combination of diffusive and hyperbolic transport. We analyze a new class of Hamilton-Jacobi equations arising from the convective part of general Fokker-Planck equations ruled by a non-negative diffusion coefficient that depends on the unknown and on the gradient of the unknown. We explore the main features of the solution of the Hamilton-Jacobi equations that contain shocks and propose a suitable numerical scheme that approximates the solution in a consistent way with respect to the solution of the associated Fokker-Planck equation. We analyze three model problems covering d…

Linearly implicit-explicit schemes for the equilibrium dispersive model of chromatography

2018

Abstract Numerical schemes for the nonlinear equilibrium dispersive (ED) model for chromatographic processes with adsorption isotherms of Langmuir type are proposed. This model consists of a system of nonlinear, convection-dominated partial differential equations. The nonlinear convection gives rise to sharp moving transitions between concentrations of different solute components. This property calls for numerical methods with shock capturing capabilities. Based on results by Donat, Guerrero and Mulet (Appl. Numer. Math. 123 (2018) 22–42), conservative shock capturing numerical schemes can be designed for this chromatography model. Since explicit schemes for diffusion problems can pose seve…

Generalization of a finite-difference numerical method for the steady-state and transient solutions of the nernst—planck flux equations

1985

Abstract A generalization of the numerical method of Brumleve and Buck for the solution of Nernst—Planck equations when convective flux and electric current are involved has been developed. The simulation procedure was applied to a specific case: transport of strong electrolytes in a wide-pore membrane with simultaneous diffusion, convection and electric current. Good agreement was found between experimental data and computed results.

A constructive theory of shape

2021

We formulate a theory of shape valid for objects of arbitrary dimension whose contours are path connected. We apply this theory to the design and modeling of viable trajectories of complex dynamical systems. Infinite families of qualitatively similar shapes are constructed giving as input a finite ordered set of characteristic points (landmarks) and the value of a continuous parameter $\kappa \in (0,\infty)$. We prove that all shapes belonging to the same family are located within the convex hull of the landmarks. The theory is constructive in the sense that it provides a systematic means to build a mathematical model for any shape taken from the physical world. We illustrate this with a va…

Granulometric analysis of corneal endothelium specular images by using a germ–grain model

2007

Specular microscopy is widely used to study the human corneal endothelium status in vivo. In this paper, the corneal endothelium is represented as a binary image composed of the cell inscribed circles. The granulometric distribution function of the complement of this image is used as a functional descriptor, which provides information about the shape, size and spatial arrangement of cells. Experimental evaluation using bootstrap techniques shows its ability to discriminate between controls and pathological cases. It represents a reliable and graphical alternative to the classical indices (cell density, hexagonality and coefficient of variation of cell areas), which behave poorly when detect…

Signorini problem with Coulomb's law of friction. Shape optimization in contact problems

1992

Thermo-Elasto-Hydrodynamic Analysis of a Crankshaft Journal Bearing

2006

This paper summarizes the essential parts of a numerical analysis activity in which the application of the Thermo-Elasto-Hydro-Dynamic (TEHD) lubrication theory to a crankshaft journal bearing is examined. The study is carried out through numerical computations performed by a commercial flexible-multibody code which simulates the lubricated contact between elastic bodies in large displacement motion. A multibody model has been created and its thermal behaviour has been validated by comparison with experimental temperatures. The validated model is used to perform two comparative analyses between the TEHD modelling and the Elasto-Hydro-Dynamic (EHD) modelling for max torque and max power cond…

Numerical analysis of composite plates with multiple delaminations subjected to uniaxial buckling load

2006

Abstract In this paper the buckling and post-buckling behaviour of unidirectional and cross-ply composite laminated plates with multiple delaminations has been studied. Finite elements analyses have been performed, using a linear buckling model, based on the solution of the eigenvalues problem, and a non-linear one, based on an incremental-iterative method. With non-linear method large displacements have been taken into account and also contact constraints between sublaminates have been added to avoid their interpenetration. It has been found that both delamination length and position and stacking sequence of the plies influence the critical load of the plate; furthermore, linear and non-li…